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Heterogeneous adaptive expectations and cobweb phenomena

  • Domenico Colucci

    ()

    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

  • Vincenzo Valori

    ()

    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

We study a cobweb-type commodity market where n firms operate and characterised by a strictly monotone demand and supply. The firms are assumed to differ in a key parameter governing price expectations which we suppose to be adaptive. We characterise the unique steady state of the resulting economic dynamics in terms of stability and we study the impact of the number and diversity of firms: to this end we introduce the notions of structural and behavioural degree of instability which prove to be crucial in determining whether stability or instability prevail. We also consider the case of market merging and establish conditions to have stability (or instability) in the aggregated market in terms of the original (structural and behavioural) degrees of instability. We take up the issue of transitional dynamics and speed of convergence when the system is stable and characterise parametric configurations that maximise the speed of convergence. Motivated by the difficulty to actually observe expectations, whereas it is easier to measure some structural features of a given market, such as the relevant demand and supply price elasticities, we take the perspective of an observer (e.g. a policy maker) whose information set includes the structural but not the behavioural degree of instability. We therefore assume the firms - via the parameter which defines their expectations - are sampled independently from a population described by a given probability distribution. In this case the structural degree of instability determines how the number of potentially different firms affects the probability of ending up with a stable outcome. Analytical results are provided alongside numerical evidence.

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File URL: http://www.disei.unifi.it/upload/sub/pubblicazioni/repec/flo/workingpapers/storicodimad/2009/dimadwp2009-01.pdf
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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2009-01.

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Length: 21 pages
Date of creation: Mar 2009
Date of revision:
Handle: RePEc:flo:wpaper:2009-01
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  1. Ely�s Jouini & Clotilde Napp, 2007. "Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1149-1174.
  2. Chiarella, Carl & He, Xue-Zhong & Hung, Hing & Zhu, Peiyuan, 2006. "An analysis of the cobweb model with boundedly rational heterogeneous producers," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 750-768, December.
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  10. Manzan, S. & Westerhoff, F., 2002. "Heterogeneous Expectations, Exchange Rate Dynamics and Predictability," CeNDEF Working Papers 02-14, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  11. William A. Branch, 2004. "The Theory of Rationally Heterogeneous Expectations: Evidence from Survey Data on Inflation Expectations," Economic Journal, Royal Economic Society, vol. 114(497), pages 592-621, 07.
  12. Herrendorf, Berthold & Valentinyi, Akos & Waldmann, Robert, 2000. "Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity," Review of Economic Studies, Wiley Blackwell, vol. 67(2), pages 295-307, April.
  13. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
  14. Bill Branch & George W. Evans, 2003. "Intrinsic Heterogeneity in Expectation Formation," University of Oregon Economics Department Working Papers 2003-32, University of Oregon Economics Department, revised 04 Oct 2004.
  15. Negroni, Giorgio, 2003. "Adaptive expectations coordination in an economy with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 117-140, October.
  16. Chavas, Jean-Paul, 2000. "On information and market dynamics: The case of the U.S. beef market," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 833-853, June.
  17. Jouini, Elyès & Napp, Clotilde, 2007. "Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs," Economics Papers from University Paris Dauphine 123456789/78, Paris Dauphine University.
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